[Preface]

The labor theory of value has historically given a tremendous moral
authority to the working
class struggle, and it has provided activists with a scientific
analysis of many features of the
capitalist economy. The Marxist elaboration of the labor theory of
value gives insight into the
basic way in which capitalist firms operate, the exploitative nature of
capitalism, the origin of
profit in surplus-value, the constant need of the working class to
fight over and over again to
maintain gains it thought it had achieved, and that ensuring that goods
are always priced at their
value wouldn't emancipate the working class. So it's not surprising,
given the desire of pro-capitalist economists to defend the capitalist
system, that most bourgeois economists have sought
to discredit the labor theory of value. Many thought they had found the
Achilles heel of Marxist
economics in the discussion in vol. III of Capital of how the
tendency towards the equalization
of the rate of profit causes the prices of goods to systematically
deviate from their value. They
claim that the mere fact of this deviation refuted Marx, and fuss over
minor defects in Marx's
presentation of the matter. This is the famous "transformation
problem".

This article corrects a defect in the mathematical side of Marx's
discussion of the transformation
problem and modifies certain of the formulas he gave. In doing so, it
doesn't undermine, but
strengthens the case for Marx and Engels' overall view of the
transformation process. Among
other things, those mathematical results of the past, which have been
taken as refuting Marx, turn
out to be in line with the labor theory of value.

Most activists haven't paid much attention to the controversy over
the transformation problem. It
has appeared to them as an obscure secondary issue. And in fact, this
common sense attitude is
quite reasonable. The basic proof of the law of value lies in the
repeated verification of the basic
features of capitalism that it explains, not in the precise calculation
of prices of production.
Moreover, most of the literature on the transformation problem hasn't
been very enlightening.

This article too will have some dry and technical matters. But I
hope to express the main
modification needed of Marx's calculations with regard to the
transformation process briefly and
clearly. And I will also seek to connect the transformation problem to
some present-day issues of
importance in their own right:

The persistence of the basic laws of capitalism despite their
continually varying forms.

The refutation of "true cost" pricing.

The "vagueness", and what Marx regarded as the "non-natural"
nature, of all marketplace
measures, whether financial categories or value.

Introductory material

Some preliminaries

This section will run briefly through some basic formulas and
concepts from the labor theory of
value that are needed in discussing the transformation problem. The
plan is to accustom the
reader to the terminology and abbreviations used in this article, while
leaving the reader to
consult Capital for the precise definition of, or elaboration
on, the various terms.

The value, or labor-content, of a product is the socially-necessary
number of hours that go
directly or indirectly go into its production. This means not just the
immediate labor used in the
final stage of production, but also the labor embodied in the raw
materials, the machines and
workplace buildings, etc.(1)

Thus, under very general conditions the exchange-value of a product
(the average price over a period of time) will be its
value, val:

val = c + v + s.

Here lowercase c stands for a certain part of
"constant capital" or capital invested in material
goods rather than immediate, living labor. It is that part of the
constant capital which is used up
during the production cycle that creates the final product and whose
value passes into the
product. It consists partly of capital invested in goods that are
completely used up in production:
I'll call this r, because raw materials are one
example of it. This is the "circulating constant"
capital.(2) And then
there is the "fixed" capital (such as machinery, buildings, etc), or
capital that
lasts longer than a single production cycle and only gradually gets
used up. I'll call the value of
the part of the fixed capital that gets used up in a single cycle w,
as it is the worn-out part of the
machinery, buildings, etc. The value of the rest of the fixed capital
is the "persistent fixed
capital" which survives to serve in additional cycles of production,
and I'll call it f for "fixed".
So the total material capital, both fixed and circulating, used in
production of the product is

f + w + r.

But only the circulating part, w + r, passes over into the value of
the product, so

c = w + r.

v + s represents the hours of labor by the workers.
The workers' do not get back in wages a
money equivalent for this entire value; instead, this value divides
into two parts. v stands for
the variable capital, which represents the wages which are paid to the
workers. If the workers are
paid the value of their labor-power, it represents the amount of value
or labor-time presented by
the goods needed for the sustenance of the workers and their families.
It's called variable capital
as the capitalists see this part of their capital grow during the
production process, in the sense
that labor adds more to the value of the product than the value of the
wages the workers receive
from the capitalists. s stands for the surplus value,
which is the excess of the value added to the
product by the workers' labor over what the workers get paid; this
excess is appropriated by the
capitalist. It is the profit made by the capitalist, if everything
including the workers' labor is
bought and sold at its value.(3)

Marx calls s/v the rate of surplus-value: it is
the ratio of the amount of money made by the
capitalist to what the workers are paid. Or more simply, it is an index
of exploitation.

The rate of profit is calculated differently. It is calculated by
comparison to the total capital
employed by the capitalist in producing the object. So this is

These formulas give rise to a curious result. If everything is
bought and sold at its value, a
capitalist's profit is proportional to the amount of the variable
capital, but has no relation to the
amount of constant capital. Thus the more variable capital that is
employed, the higher the total
profit and the rate of profit, but with more constant capital, the
profit stays the same and the rate
of profit is lower. Thus the return on capital will differ from one
enterprise to another. In this
discussion, I'm assuming for simplicity that the rate of exploitation
(s/v) is the same for all
capitalists. Then comparing two capitalists in different fields, who
both used the same amount of
total capital, the one with more workers would have a higher rate of
profit than the one with
fewer workers.(5)

Thus the rate of profit will depend on the ratio between the
constant and the variable capital used
in production: this is what Marx calls the "organic composition" of the
capital. A high organic
composition is what is known in bourgeois economics as being
"capital-intensive", although
actually variable capital is capital too, and a low organic composition
is known as being "labor-intensive". If prices averaged around their
values, a high organic composition of capital would
correspond to a lower than average rate of profit, and a low organic
composition would
correspond to a higher than average rate of profit.(6)

But if capital can flow from one field to another, then there will
be a tendency for the rate of
profit to equalize among capitalists. This requires that the prices be
determined in a different way
from what has just been described. For the rate of profit to tend to be
equal, the prices of
products should tend toward the so-called "prices of production" (pp).
They are calculated as
follows:

First one considers the cost-price (k) to the
capitalist of producing some good. This is just c + v,
which gives the cost of the materials used up in production plus the
workers' wages. If the
general rate of profit is R, then the profit should
be R times the total capital employed in
production, including all the fixed capital, or R(f + c + v), which can
also be written as R(f + k).
Hence

pp = k + R(f + k) = (c + v) + R(f + c + v)

=Rf + (1 + R)(c + v)

Well, this formula has to be taken over the entire output of that
particular item during a
production cycle. To see this, consider the case of a machine that
costs a million dollars
producing hundreds of thousands of items during a production cycle,
with a general rate of profit
of 10%. Rf is $100,000, and Rf is only part of the price of production.
So if one applied this
formula to one item, it would seem to say that a single item costs more
than $100,000. But in
fact, if 200,000 items are produced with the help of this machine in
the course of a production
cycle, then one has that the total price of production of all these
200,000 items is more than
$100,000. Well, that means that the term Rf only adds $.50 to the
course of each item. That
explains why expensive machines can be used to produce cheap products.

Alternatively, let N be the number of units of the
product that the machine produces in a year. If
one wants to use the formula with respect to individual units of
output, one lets

f=(value of machine)/N.

The important point about the formula for pp is that values and
prices of production differ. This
is the starting point of the transformation problem, as it shows that,
if there is a tendency for the
rate of return to equalize, the prices of products have to
systematically deviate from their value
or labor-content.

Adam Smith's and David Ricardo's transformation problems

The labor theory of value originated in the work of early bourgeois
economists, such as Adam
Smith and David Ricardo. Their work would at some points say that
pricing was according to
value, and at other points, that it was according to prices of
production. This was only one of the
contradictions that appeared in their work.

Since then, bourgeois economics has been unable to deal with this
issue. Instead, it degenerated
into apologetics for capitalist exploitation and gave up the labor
theory of value.

Indeed, for a long time now bourgeois economists have mocked the
theory of value. They claim
one can avoid all the trouble and fuss surrounding the transformation
problem if one throws
away the concept of the labor value of a product and looks only at
subjective preferences for
products and their supply and demand. Accept this, and one will
supposedly enter the realm of
clear and straightforward economics. This claim might have a certain
resonance among people
sick of the widespread quibbling over the transformation problem.

Yet, despite such claims, bourgeois economics is extremely
complicated and full of ever more
elaborate and obscure mathematical formulae. Nothing was solved by
throwing out value, and
the issues involved were simply swept under the rug. As time went on,
bourgeois economists
discovered that their financial indices were subject to what they call
the "aggregation problem",
the "index problem", and even such an obscure term as "the Cambridge
capital controversy".
They wring their hands in many obscure and highly mathematical tomes
about this, but when
talking to the general public, they deal with these contradictions in a
much simpler manner --
they ignore them. But this takes us too far ahead of ourselves in this
story. We'll come back to
the aggregation and index problems and the Cambridge capital
controversy later in this article.

Marx and the transformation process

It was one of the strong points of Marx's approach that he noted
this and other contradictions in
the labor theory of value as developed by Smith and Ricardo, and
developed a more scientific
version of it. He pointed out that the tendency to the equalization of
the rate of profit leads to a
systematic deviation of prices from values.

Unlike what is pictured by critics of Marxism, this was not a
particularly hard step for Marx to
take. He had always noted that exchange-value and individual prices in
the marketplace
deviated, both because exchange-value represented an average price
under general conditions,
and because monopoly, shortages, absolute (but not differential) land
rent, government
regulations, and so forth caused deviations from value. Marxist
economics analyzed and
explained these deviations using the law of value, and reached useful
conclusions about them.
What was different with respect to prices of production was only that
here was a systematic
deviation of a more universal character.

So it was natural for Marx to realize that the equalization of the
rate of profit modified the way
that the law of value was manifested in marketplace prices, but didn't
overthrow it. The
transformation to "prices of production" results in the surplus-value
exploited from the working
class being redistributed among the capitalists: some firms, those
employing capital with a high
organic composition, would appropriate to themselves not only the
surplus-value they exploited
from their workers, but also some of the surplus-value sweated out of
the workers by other
capitalists, while those firms employing capital with a low organic
composition would give up to
other capitalists some of the surplus value they exploited from their
own workers. Only for those
firms employing capital of an average organic composition would profit
and surplus value
coincide.

Marx held that, nevertheless, the labor-value of commodities
dominated the formation of prices
of production; surplus-value explained the origin and size of profits
and the rate of profit; and
changes in value were responsible for the main changes that took place
in the prices of
production. Thus volume III of Capital, which deals with the
equalization of the rate of profit,
showed that the conclusions reached in volumes I and II of Capital
remained valid, while also
bringing some additional features of capitalism into focus. Among other
things, Marx pointed
out that the sharing out of the pool of surplus-value among capitalists
according to the size of
their capital helps explain their class solidarity against the working
class, as the extent of the
profit obtained by an enterprise depends not only on what the
individual capitalist exploits from
the firm's workers, but also on what all the capitalists, as a class,
have exploited from the
working class as a whole.

The helper formulas for the transformation process

In Volume III of Capital, Marx gave some formulas
concerning the transformation process. They
provide an intuitive approach to seeing how the transformation process
works. These include the
following:

The sum of the prices of production in all spheres of production
equals the sum of the value of
all the products.

The sum of the profits in all spheres of production equals the
sum of the surplus value.

He implicitly takes it that the rate of profit is the same if
calculated in value terms or in terms
of the prices of production.

He also sets forward that the prices of production can be calculated
from the values by the
formula I have mentioned above, which if the persistent
fixed capital is taken for simplicity to
be zero, is:

pp = k + Rk = (1 + R) k = (1 + R) (c + v).

However, he also noted that ". . . We had originally assumed that
the cost-price of a commodity
equalled the value of the commodities consumed in its
production. But for the buyer the price of
production of a specific commodity is its cost-price, and may thus pass
as cost-price into the
prices of other commodities. Since the price of production may differ
from the value of a
commodity, it follows that the cost-price of a commodity containing
this price of production of
another commodity may also stand above and below that portion of its
total value derived from
the value of the means of production consumed by it. It is necessary to
remember this modified
significance of the cost-price, and to bear in mind that there is
always the possibility of an error
if the cost-price of a commodity in any particular sphere is identified
with the value of the
means of production consumed by it."(7)

This means that the formulas given above have to be modified. I have
defined various things,
such as the constant capital, the variable capital, and so forth, with
respect to their values. Now it
is necessary to consider the same categories, but calculated according
to their prices of
production. So, for example, I am using c to refer to the value of the
constant capital. Let's use c
to refer to how much the constant capital costs when calculated
according to the prices of
production of all its components. In general, I'll use
underlining to indicate that a category
should be calculated via the prices of production.(8)

Thus the formula for the price of production becomes

pp = (1 + R ) k = (1 + R) (c
+ v).

Marx held that the rate of profit is the same whether calculated in
value terms or prices of
production, i.e. that R = R, so the above formula reduces to

pp = (1 + R) k

(I'm using pp to indicate the approximate value for the price of
production which results if one
calculates with the values, and pp to indicate the precise
price of production.)

Marx's formulas provided an appealing way to approach the
transformation issue. However,
some of these formulas turned out to be only approximate, and later in
this article I will show
how they have to be modified. This doesn't undermine Marx's overall
view, because these
approximate formulas are only helper formulas, not key assertions. If
their more accurate
versions also back the key assertions, as in fact is the case, then
these modified formulas
strengthen, rather than weaken, the Marxist view of the transformation
issue.

Mathematical difficulties

The fact that the more accurate formulas for prices of production
involve underlined quantities
gives rise to two mathematical difficulties which were used to cast
doubt on the Marxist view of
the transformation process. The first difficulty concerns calculating
the prices of production in
terms of value, and the second concerns some of the helper formulas.

To begin with, pp can be calculated easily and directly from the
values via the formula pp = (1 +
R)k, but that is not so for the precise prices of production via the
formula pp = (1 + R) k. This is
because the latter formula involves relations between the
prices of production of different
products, rather than relating the price of production of a single
product to the values of other
products, and it also requires finding the transformed rate of profit.
So the second formula
doesn't directly give the price of production in terms of values.

In practice, one can probably obtain a suitable approximation fairly
easily in most cases.
Moreover, in any real economic situation, an approximation is indeed
the best one can obtain.
Marx, for example, noted repeatedly that there is only a tendency to
achieve a uniform rate of
profit, not an exact equalization of the rate of profit. And he also
noted that various fields of
production ended up left out altogether from the equalization of the
rate of profit. These
phenomena in themselves undermine the exactness of any formula based on
assuming that the all
rates of profit are equalized.

So it's not clear why a precise formula is that important. In
practice, one needs to know the
general way in which the transformation from values to prices of
production affects the
distribution of profits among firms and affects what is produced and
what is not produced. One
also needs to know in what type of economic problems one can directly
apply values, leaving
aside the transformation to prices of production as an irrelevant
complexity, and in what type of
problems one has to consider this transformation. But one rarely needs
to know the precise
number of abstract labor-hours represented by any product.

However, some economists wouldn't believe that value could determine
the prices of production
unless a more precise mathematical analysis was given. While I disagree
with this, the point is
moot, since it turns out that such an analysis would eventually be
given.

But, as this analysis emerged, the transformation problem went into
a new phase, because it
turned out that some of the helper formulas were only approximations.
Simple mathematical
models of an economy were analyzed. Simultaneous equations were used to
solve for prices of
productions. It was determined that one could either set the total of
the prices of production
produced in all spheres or production to the total of the value of
everything produced, or one
could set the total of the profits in all spheres of production to the
total of the surplus value in all
spheres. But one couldn't, except in special cases, have both these
helper formulas of Marx
satisfied: that is, they both couldn't be completely satisfied -- it
wasn't considered sufficient to
have them both approximately satisfied. In this article, I
will, unless otherwise noted, always
take the total of the prices of production to be equal to the total of
the values. This is always
possible according to the mathematical models, and by doing this one
avoids having to worry
about defining the standard of money: the equating of the total prices
to the total values
accomplishes this automatically. The issue of defining the standard of
money adds confusion and
complexity to many discussions of the transformation problem, and yet
is irrelevant to its
solution.

The critics of Marxist economics took these developments as a
refutation of the law of value, and
a voluminous and obscure literature on this question has developed.
Their point of view was that
if the helper formulas weren't exact, then Marxist economics collapses.
It didn't matter whether
the formulas were a reasonably good approximation of economic life;
such a question was not of
interest to them. Instead they held that, unless these formulas were
exact, the whole edifice of
Marxist economics was without foundation. For example, if the sum of
the profits in the whole
economy wasn't equal to the sum of the surplus value, it would show
that profit was created in
some other way than exploitation via surplus value.

This brings me to the end of the introductory
material. In the next part of the article I will put
forward a refinement of some of the helper formulas that ensures that
they all are exact. This
modification follows from a closer look at the law of value, rather
than contradicting it. This
should remove a theoretical objection to the law of value that was
bothering some activists, and
vindicate the Marxist approach. It also has some useful theoretical
implications with respect to
current controversies concerning "true value" and financial
calculation.

An overlooked feature of value

The money/value relationship and individual products

Marx pointed out that the equalization of the rate of profit
required that products sell above or
below their value, depending on the organic composition of the capital
used to produce them.(9)
So if two items, A and B, both represent the same value, A might sell
for $100, while B sells for
$200. But this means that when one spends $200 in the marketplace, if
one spends it on B, one
gets a product with a certain amount of value, but if one spends it on
A, one could buy two A's
for that $200 and thus take home products worth twice the value than if
one were buying B's.
Thus, if things are selling at their price of production, the
amount of value represented by a sum
of money depends on what product is bought with it. To be
more precise, it depends on the
organic composition of the capital used in producing the item.

It's useful to express this in mathematical symbols. If everything
sold at its value, then the
amount of value represented by a certain amount of money would be equal
to

vallh = L·m

where vallh is the
value measured in labor-hours, m is the amount of
money in dollars, and L
is
the ratio of value to the price of an item. So L is how much value,
measured in units of socially-average labor (abstract labor-time), is
represented by $1. So if $1 represents 2 minutes of labor-time (1/30th
of an hour), then L = 1/30 labor-hour per dollar; and if some product
costs $15, then
the value in labor-hours of that product is 15(1/30) = ½ an hour.

This formula has the inverse

m = D · vallh

i.e. the amount of money spent on items is so much
times their value, where D is the ratio of the
price to the value, with the value measured in labor-hours. D = 1/L,
represents how many dollars
a product worth a socially-average labor-hour will sell for. Recalling
that $1 represents 2
minutes, and L = 1/30 labor-hour per dollar, then D = 30 dollars per
labor-hour, so a product
with a value of 2 labor-hours would cost 2 · 30 = $60.

When things are sold at their price of production, these formulas
change, and in particular, they
break up into many formulas. In these new formulas, m will be
underlined to indicate that it
refers to prices of productions. Depending if one is buying A's or B's,
one has

vallh = LA·m or vallh = LB·m.

More generally, one has

vallh = Lproduct·m

where Lproduct is a number depending on
the organic composition of the capital used to produce
that particular product. L is the ratio of the value of product,
measured in labor-hours, to the
price of production. And similarly,

m = Dproduct·
vallh,

where Dproduct is the ratio of the
price of production to the value of a product, measured in labor
hours.

For example, recall that a single unit of A and a single unit of B
both have the same value.
Suppose that value is 5 labor-hours. Then, recalling that a single A
costs $100, 5 = LA· 100, so
LA = 1/20=.05 labor-hour per dollar. Similarly, recalling
that a single B costs $200, 5 = LB· 200,
so LB = 1/40 = .025 labor-hour per dollar. Thus L, the
amount of value represented by a $1,
might average out at 1/30=.033 in general, but LA, the
amount of value represented by $1 spent
on item A's, is .05, and LB, the amount of value represented
by $1 spent on item B's, is .025.

Similarly, D, the amount of money which an item with a value of 1
labor hour costs, might be
$30 on the average. But when one is buying A's, m = DA· vallh, so 100 = DA· 5. Thus DA
= 20,
and one can similarly see that DB = 40.

Thus in place of a single L, good for all products, there are a
large number of Lproduct's, one for
each product. And similarly for D.

Well, one might be buying quite a few different types of items with
a sum of money, in which
case one has

vallh = LA· mA
+ LB·mB + LC·mC + and so on,

where mX is the amount of money
spent buying item X's, and the total amount of money m = mA
+ mB + mC + and so on. This could
also be expressed also

vallh = Lshopping basket·
m

where Lshopping basket is the average
of the L's for different items that is bought with the money,
weighted according to how much money was spent on them.

For example, suppose one spends $300 to buy two items: one A and one
B. Then the resulting
value vallh=.05 · 100 +.025 · 200 = 5 + 5 =
10 labor hours. This could be expressed as 10 =
Lshopping basket· 300, so Lshopping basket
= 1/30 = .0333 labor-hour per dollar, where Lshopping basket.
thus
represents some kind of average of .50 and .025. But suppose one had a
different shopping
basket of $500 which is to be used to buy three items: one A and two
B's. One could do a similar
calculation and end up with 15 = Lshopping basket 2· 500,
so Lshopping basket 2 = 15/500 = .03, instead of
.033. Thus Lshopping basket depends not just on which
commodities are in the shopping basket, but on
how much of each commodity is there.

Lall would be the L when the shopping
basket includes everything. This is an L which is
averaged out for the entire economy, so I might also call it Laverage.
The other L's, or LX's, would
vary, some being higher than L = Laverage and some lower.
Similarly, the original D in this section
is the same as Dall=Daverage.

Marx and Engels pointed out that a capitalist economy never directly
estimates values in terms
of the number of labor-hours they represent, but instead makes this
estimate indirectly in terms
of exchanges between different products and money. And in discussing
the transformation
problem, in Capital and various other places, the amount of
value is measured in money rather
than hours. So it will be of use to discuss the variations in how much
value is represented by a
sum of money in terms of val, which differs from vallh in
that it is expressed in dollars. This is
done by measuring labor hours by using the average amount of dollars
represented by a
labor hour. Thus

val = Daverage· vallh.

Recall that I have been using, as an example, that Daverage=Dall
= $30 per labor-hour. So, if
something has a value of three-labors, then it can also be measured as
a value of 30 · 3 = $90
dollars. The difference between measuring value in abstract labor-hours
or in the average amount
of dollars represented by a labor-hour is like the difference between
measuring distance in yards
or feet. A certain length might be described as either 3 yards or 9
feet, and a certain value might
be described as either 3 labor-hours or $90.

Note that one uses the same D=Daverage= Dall
as the conversion factor no matter what product's
value is being measured. The difference in dollars per labor-hour which
occurs in prices of
production are not reflected in val, as val is a measure of value, not
of the price of production. In
order to deal with the deviations caused by prices of production with
respect to val another
formula is needed.

To get this formula, recall that vallh = LX·
m. And so val = Dall· vallh =
Dall (LX· m) = (Dall·
Lx)
m. Now let UX = Dall·
Lx. The result is that

val = UX·m

where val is the amount of value, measured in
dollars, represented by the sum of money, m, used
to purchase item X at its price of production, and UX is the
ratio between the value and the price
of production of the product X.

For example, recall that item A has a value of 5 abstract
labor-hours. Its price of production, m,
the amount of money needed to purchase it, is $100. Also $100=DA· 5. So DA = 20. But its value
measured in dollars is Daverage · 5, not DA· 5, and Daverage was taken above as $30 per
abstract labor
hour. So the value measured in dollars would be 30 · 5 = $150,
not $100. Now, from the equation
$150 = UA · $100, it turns out that UA=1.5.
UA being greater than 1, as it is here, means that the
value of A is greater than its price of production. Thus UA
is a measure of the deviation between
prices of production and values; if UA is greater than one,
the value is higher.

Now, item B also has a value of 5 abstract labor-hours, but its
price of production m is $200 =
DB· 5. Thus DB = 40. But its value
measured in dollars is Daverage· 5, not DB· 5, and Daverage = $30 per
abstract labor hour. So the value measured in dollars is 30 · 5=$150,
not $200. And, from the
equation $150=UB· $200, it turns out that UB
is .75. This illustrates that UB being less than one
corresponds to the value of B being less than its price of production.

If UX = 1, then val = m, i.e. the value and the
price of production are identical.

The inverse of the formula for UX (the ratio of value to
price of production) would be a formula
that gave the amount of m for a given amount of val, rather
than the amount of val for a given
amount of m. Instead of val = UX·m,
one would have m = (1/UX) · val. Define TX
as equal to
1/UX, and the following formula results:

m = TX· val

where TX, the ratio of the price of
production to the value (measured in dollars), shows how
much the price of an item is changed when one passes from values to
costs of production. I use
the letter T here, for transformation,
since the transformation problem is often regarding as
finding the formula for the prices of production of things, given their
values.

Well, the total of the prices of production for all spheres of
production is equal to the total value,
so mall = valall. But also mall
= Tall· valall , so Tall
= 1. In general, TA will vary according to the
organic composition of the capital used in producing item A. TA
is less than one when A is
produced in a labor-intensive sphere of production, and greater than
one in the capital-intensive
situation.

By now, the reader may well be getting impatient. All this may
appear as much ado about
nothing. Surely, the reader may think, just about anyone who did much
work on the transformation problem must have been aware of these simple
formulas. Perhaps. Didn't these
theorists refer to the price-value deviations for various individual
products? Of course. But they
viewed the gist of the transformation problem as finding a way around
these deviations, a way to
aggregate them out of existence in the helper formulas by considering
whole sectors of
production rather than individual products. They generally didn't want
to ponder the significance
of the fact, reflected in these formulas, that the value of a sum of
money remained indefinite until
it was exchanged for a product; they wanted to brush this aside.

There are, indeed, some things that might lead one to overlook this
significance. For one thing,
the different L's (ratio of value to price) wouldn't usually vary
anywhere near as much as they
do for the hypothetical items A and B above, where A had same value as
B, though B costs twice
as much. Moreover, usually a sum of money is spent buying many items,
so the L for the entire
sum of money (the aggregate L, so to speak), as the average of many
constituent L's, would
come close to Lall, and the aggregate T (ratio of price to
value), as the average of many
constituent T's, would come close to Tall = 1. For this and
other reasons, in most practical
problems one can brush aside all these L's, D's, U's and T's.

Also, although this article is inspired by Marx and Engels's work
and vindicates their approach
to the transformation problem, they didn't talk about the relationship
of price and value in quite
this way. This article brings out an aspect of the Marxist analysis of
value, namely a certain
indeterminacy and vagueness in value, that was implicit in Marxism from
the start, but Marx
expressed it in different ways from what is said here. One way he did
this was by stressing that
value, the abstract labor-hour, was a category that glossed over the
qualitative differences
between different sectors of production and different products,
differences which had to be taken
into account in the economic planning of a classless society. I will
come back to this point later
in the article when I discuss Marx's view that value is a "non-natural"
category.

The relation of the total profits to the total surplus value

Now let's apply these relations to the transformation problem. The
equality of the total surplus
value and the total profits is one of Marx's helper formulas, and it is
a formula which was
challenged by subsequent mathematical work. A good deal of the
literature on the transformation
problem revolves around this question.

The mathematical models which are used to calculate the price of
production from values specify
that the total physical quantity of goods
bought, when everything is priced at their value, by the
capitalists with their profits remains the same when things are priced
at prices of production.
Each enterprise and sphere of production continues to produce the exact
same products, and in
the same physical amounts, as before. But
these models allow the amount of the profits which
any individual capitalist obtains to vary
(which corresponds to a redivision of the surplus value
among the capitalists). However, they don't allow any variation in the
total amount of goods
which are bought by the capitalists as whole with these profits. But
although the total physical
amount of goods purchased by the profits are the same before or after
the transformation from
pricing at value to pricing at prices of production, the total price
of this physical amount of
goods changes (except in special cases).(10) This result for the total profits
expressed in dollars
was obtained over and over again by mathematicians and economists.

Now, when goods are bought and sold at their value, the profit
obtained by any firm is identical
with the surplus-value which it extracts from its workers. So in that
case, the total profits equals
the total surplus-value. Thus the change in the total profits, from the
situation where goods sold
at their values to that where goods are sold at their prices of
production, means that the total
surplus value doesn't equal the total profit (calculated at prices of
production), except in special
cases. And this directly contradicts Marx's helper formula.

But Marx's derivation of this helper formula implicitly relied on
the idea that the variation of the
T's can be ignored. The idea is presumably that as the total profits
come from all spheres of
production, one can assume that Ttotal profits = 1, as Tall
= 1. But while the profits may come from
the factories and other workplaces in all spheres of production,
enterprises that produce
everything in the whole economy, the profits are spent
only on a part of the output. The sum of
goods indicated by the subscript "total profits" is not the same as the
total economic output
indicated by the subscript "all". Thus there is no reason to assume
that Ttotal profits = Tall.

For example, consider the following simple but often-used model of
an economy with three
sectors or spheres of production: one sector produces means of
production, a second produces
means of consumption, and a third produces luxury goods that are bought
only by capitalists.
Assume that the capitalists spend all their profits on luxury goods
(this is a model of a static
economy, which continues unchanged from year to year as the capitalists
never invest in
expanding production), and that only capitalists buy these goods. Then
the mass of profits will
correspond to the total output of these goods, and only these goods.

Thus the profits will be spent on one sector of production only, the
third or luxury sector, and not
on either of the other two sectors. Therefore Ttotal profits
will depend on the organic composition of
simply one sector, that of luxury goods; in this model, Ttotal
profits = Tluxury sector. And there is no
reason that the sector producing luxury goods would have an average
organic composition. True,
in practice, in most real economies of any substantial size and
complexity, there might be good
reason to believe that its organic composition didn't differ that much
from the other spheres. But
there is no reason to believe that it would be precisely the same. So,
except in special cases, Ttotal
profits wouldn't be equal to one. This is the crucial point. But
to express this clearly, a few
additional formulas will be useful.

Let S be the total surplus value produced in the
entire economy, and in general I'll use
capitalized categories to indicate those that refer to the entire
economy or to large branches of
it. So, similarly, let P be the
total profits produced in the entire economy. In the economic
models used in discussing the transformation problem, the total surplus
value and the total profit
refers to the same physical amount of goods, only the surplus value
represents the total value of
these goods, while the profits refer to the total of the prices of
production of these goods. (In the
case of the three-sector model I have been discussing, these goods are
the total output of the
luxury sector.) So P and S, the total profits and the
prices of production of the goods representing
the surplus value, are the exact same thing: P = S.(11)

Now, recalling that T refers to a ratio between prices of production
and value, the amount of
total profits, measured in dollars, is given by the following formula:

P = S = Tluxury sector·
S .

Or, to express it in a form which generalizes better,

P = Ttotal profits·
S.

Now, since Ttotal profits is not equal to 1 in this
model, except for the special case in which the
sphere of luxury good production has the average organic composition,
the total profits and the
total surplus value differ when expressed in dollar terms.

But wait! How can the same physical amount of goods, the output of
the luxury sector, be
expressed by two different prices? It's because the surplus value
represents these goods priced as
if all goods were priced at their values. But the total profits
represents these same goods, when
they are priced at their prices of production. And the whole point of
the transformation process is
that the price of production of commodities usually differs from their
value.

In physical terms, and also in terms of value, the capitalists as a
whole (not the individual
capitalist) get the same total amount of profits before or after the
transformation to prices of
production. Individual capitalists may get more or less profits,
whether in physical terms, value,
or price, as the profits are redivided in order to obtain an
equalization of the rate of profit. But
the total profits remain the same in physical terms and value, and the
difference in price reflects
only the change from evaluating a certain quantity of goods by its
value or by its price of
production.

Marx's view was that the total surplus value or total profits
remained the same but was
redistributed in a different way. That is so, as expressed in both
value and physical terms. It is
not exactly so when one measures by prices (except in the special case
when Utotal profits = 1). But
this modification of Marx's helper formula doesn't affect the overall
deductions which Marx
made with regard to the transformation issue.

Actually, since Utotal surplus value (and Ttotal
profits = 1/Utotal surplus value) are probably usually
both close to
1, the total profits and the total surplus value are probably
approximately equal in most cases.
But the issue raised in the transformation problem was that the
slightest difference would, in
principle, undermine the Marxist theory of surplus value
by proving that some profits didn't
come from surplus value. That objection is overcome by the fact that
this difference only reflects
that the price of production and the value differ for the physical
amount of goods in which the
profits are realized, since the organic composition of the capital in
the sphere of production
producing these goods is not the same as the average organic
composition for the whole
economy.

This discussion has proceeded on the basis of a simple division of
the economy into three sectors
of production. However, the point being made is true in general. In any
economy undergoing
simple reproduction, the mass of goods can be divided into those which
replace the means of
production used up in the course of a cycle of production, those which
are means of consumption
for the workers during that cycle, and those which are purchased by the
capitalists with their
profits. But in a more general situation, those three masses of goods might not represent entirely
distinct sectors of production:
for example, the capitalists might buy with their profits, not just
luxury goods, but means of
production and/or consumption in order to expand production. Thus the organic composition
of the capital that
produces the goods bought by the profits won't be simply the organic
composition of the luxury
industries, but a weighted average of the organic composition of the
different spheres of
production involved in producing the goods representing the mass of
profits. That is the only
change needed in generalizing from the simple model of an economy to a
more realistic model.
Even if the profits were spent on some goods from every sector of
production, they still wouldn't
represent the total output of all these spheres, but only part of the
output. Thus the weighted
average of the organic composition of capital used to produce the goods
represented by the
profits still would only by accident equal the average organic
composition of the entire economy.

Thus the law of value provides, in principle,
a clear, precise, and simple relationship of the total
profits and total surplus value. To get the exact formula
for the relationship between the two
expressed in dollars, one has to calculate Ttotal surplus value.
The precise formula turns out to be
complex, and finding it requires careful mathematical calculation. But
the overlooked property
of value, the fact that the same amount of dollars can represent
different values, what I call a
certain vagueness or indeterminacy of value, clearly explains why the
dollar figures for the total
profits and total surplus value usually differ.

The rate of profit

The same considerations that apply to the total profits also apply
to the total constant capital and
the total variable capital. Just as the total profits only represents a
fraction of the mass of
products of the economy, the same goes for the total constant capital
and total variable capital.
We thus have that, measured in dollars, the price of the total constant
capital differs depending
on whether the goods making up that capital are priced at their value,
or at their prices of
production. The same goes for the variable capital. Hence, letting V
stand for the total variable
capital and C for the total constant capital, we have, not only

The rate of profit calculated when using prices of production is,
when one abbreviates Ttotal profits
as TP, Ttotal variable capital as TV, Ttotal
constant capital as TC, and Ttotal surplus value
as TS(12)

R = P /(V + C) = TP S/(TC
C + TVV)

Now, as the sum of the values of all products equals the sum of the
prices of production,

E = E = TCC + TVV + TSS

and so another formula for R is

R = (TSS)/(E - TSS).

The formulas for R and R are different, and so the rate of
profit calculated via prices of
production usually differs from the rate of profit calculated via
values. The two rates of profit
will generally be reasonably close, since TS won't usually
be that far from 1. But they will only
be exactly the same in special cases.

The modified helper formulas

So the following formulas replace the helper formulas, modifying all
those listed except the first
one:

E = E (the sum of the value of everything
equals the sum of all the prices of production)

P = TP S, not S.

V = TV V, not V.

C = TC C, not C.

R = (TS S)/(E - TS
S), not R = S/(E - S).

According to these formulas, there is no mysterious gain or loss of
profits in going from the
description of the economy via value to the description via prices of
production, just a change in
how much value equals how many dollars depending on the organic
composition of the goods
comprising the total profits. These formulas provide a suitable basis
for the transformation
process that Marx mapped out in Vol. III of Capital.

Moreover, for any large and complex economy, the various T's are
likely to be close to 1, so that
the modified formulas are quite close to the original ones. The organic
composition of any one
product may differ from that of the average, but the organic
composition of a gigantic sector of
production, such as the sector of all means of production, is likely to
have an organic composition rather close to the average for the entire
economy.

But in any case, the objection to Marx's formulas wasn't that the
observed aggregate quantities
differed substantially from Marx's formulas, but that any difference at
all would supposedly
undermine the logical basis of the theory of value. Thus the fact that
differences would appear in
the mathematical models of an economy were regarded as a refutation of
the theory of value. The
modified formulas, however, show that a certain deviation should be
expected on the basis of
the law of value. They therefore eliminate the
contradiction between the past mathematical
calculations and the theory of value.

Caveats

The above way of writings the helper formulas brings out that
their interpretation is simple in
principle, but the actual formulas for the various T's are quite
complex. I haven't gone into this
because the precise formulas aren't at stake, and many of the past
calculations of them for
various mathematical models seem to be correct. What has happened,
however, is that the
attention to the complex details of the T's helped obscure the role
that the T's actually play in
the transformation problem.

When one averages the T's to get a composite T, one uses a
weighted average. If, say, one is
considering a collection of products, consisting of three products with
prices of production m1, m2, m3,
then

I have said that Tproduct depends on the organic
composition of the capital used in producing the
product. This statement is intuitively what is going on, but there is
an added complexity. Tproduct represents the ratio of the
price of production of something to its value. This clearly depends in
large part on the organic composition of the product, because that
determines how the price of
production is related to the cost-price of the product. But, as
mentioned earlier in this article,
Marx pointed out that the cost-price of the product itself changes when
one goes over to prices of
production, and that change depends on the organic composition of the
various components that
go into producing the product. And it also depends on the cost-prices
of those components,
which in turn depends on the organic composition of whatever went into
producing those
components, and so on. Thus the price of production depends on the
organic composition not
only of the product concerned, but also of all its components, and of
anything that went into
producing those components. In a modern complex economy, quite a lot is
involved, directly or
indirectly, in the production of any one product.

Thus, one could say that it depends on the full organic
composition of the product. This is one
reason why the formula for Tproduct can be quite
complicated.

However, if one is concerned simply with how far one capitalist, due
to the equalization of the
rate of profit, obtains more or less profits than one might expect from
his own exploitation of
labor, then what matters is the organic composition expressed as the
ratio of constant capital to
the variable capital, evaluated in prices of production. And it seems
to me that in practical
problems, this is more likely to be what one is concerned about.

Nevertheless, there are three different organic compositions might
end up being considered:

(1) the organic composition
evaluated in value terms,

cproduct/vproduct,

(2) the organic composition
evaluated in prices of production,

cproduct/vproduct = (Tc
for that product/Tv for that product) (cproduct/vproduct,),

and (3) the full organic
composition, represented by Tproduct.

A certain part of the literature on the transformation problem
consists, essentially, of making a
big fuss about the difference between the full organic composition and
the organic composition.
Oh horrors, it might occur in some special case that product A has a
higher organic composition
than product B, but a lower full organic composition. That's
conceivable, but not something of
any special significance.

It might conceivably have been useful if the economists who worked
on the transformation
problem had considered finding useful approximations to the T's;
considered examples of when
products had exceptionally high or low T's, or examples of where the
organic composition and
full organic composition differed significantly; and looked into
whether this had some useful
significance in analyzing real economies. But the belief that the very
existence of the T's cast
doubt on the labor theory of value resulted in the attention being
focused simply on such things
as whether, in principle, the discrepancy between the organic
composition and the full organic
composition overthrew Marxist economics.

Relation to some past results on the transformation problem

The recognition of the overlooked property of value makes sense of
the previous results obtained
on the transformation problem. Below I remark on a few of them.

The Bortkiewicz-Sweezy results

In 1907 the neo-Ricardian economist Ladislaus Bortkiewicz published
a paper that showed, in
the case of a simple economic model and by use of simultaneous
equations, how to obtain prices
of production from values. He also showed that, in general, either the
total prices of production
wouldn't equal the total value, or the total of the profits (calculated
according to prices of
production) wouldn't equal the total surplus value. He regarded this as
an important part of his
criticism of Marx and defense of Ricardo.

In his book The Theory of Capitalist Development (1942),
Paul M. Sweezy popularized
Bortkiewicz's calculations. He used the three-sector model of the
economy used above, where
profits profits were spent on the luxury sector and only on the luxury sector. He held that
the ability to obtain the
prices of production from the values was an important verification of
Marx's transformation
process.

But it wasn't clear what his view was towards what I call the helper
formulas. He appears to
have thought it important to ensure that the total profits were equal
to the total surplus value, but
he let the total of the prices of production deviate from the total
value by using a gold standard
for money.(13) He
asserted correctly that in his system "only in the special case where
the organic
composition of capital in the gold industry is exactly equal to the
social average organic
composition of capital is it true that total price and total value will
be identical."(14)
This makes it
appear as if he didn't think the helper formulas (such as the equality
of the total prices and the
total value) would usually be satisfied.

However, he also claimed that one could overcome the deviations in
the helper formulas, writing
that "It is important to realize that no significant theoretical issues
are involved in this
divergence of total value from total price. It is simply a question of
the unit of account. If we had
used the unit of labor time as the unit of account [i.e.
the standard for money] in both the value
and the price schemes, the totals would have been the same.
Since we elected to use the unit of
gold (money) as the unit of account, the totals diverge."(15)

Sweezy's claim that he could simultaneously achieve the equality of
total prices and total values,
and total profits and total surplus value, was wrong. What he failed to
realize, or at least he
certainly failed to point out, was that, in his system, if he had
switched the money standard in
order to ensure that the total prices equal the total value, then this
would have upset the equality
of the total profits to the total surplus value.

However, Sweezy immediately goes on to add that it doesn't matter
whether the total prices
equals the total value, saying "But in either case
the proportions of the price scheme (ratio of
total profit to total price, of output of constant capital to output of
wage goods, et cetera) will
come out the same, and it is the relations existing among
the various elements of the system
rather than the absolute figures in which they are
expressed which are important."(16)
Sweezy is
correct that it is not necessary to have all the helper formulas
satisfied, but his reasoning is
wrong. For one thing, he doesn't prove, and it isn't true, that all the
relations (ratios) between the
various elements of the system will remain the same. That depends on
the organic composition
of the different sectors of the system.

So it is rather confusing whether Sweezy thought that all the helper
formulas could be satisfied,
or whether he thought it wasn't important to have them satisfied. In
any case, it seems to me that
what his calculations actually showed (as opposed to what he said about
his calculations) was
essentially that, for the simple three-sector economic model he and
Bortkiewicz used, both the
total prices would equal the total values, and the total profits
equaled the total surplus value, if
the luxury sector (on which, in the model he was using,
profits, and only profits, were spent)
had an average organic composition.

A similar view of his calculations (if not of his claims) is put
forward in a survey of the
transformation problem in the New Palgrave.
Here it is stated that "Sweezy went beyond Bortkiewicz, and claimed
that his solution would satisfy both of Marx's claims. . . .
Unfortunately,
Sweezy's success is a result of his assumptions. First, since surplus
value is equal to the output
of the luxury sector, setting this output equal to one in both prices
and values ensures that total
surplus value will equal total profit. The assumption of a socially
average organic composition in
the third sector [luxury goods] obtains the second condition [total
prices of production equals
total value]."(17)

Thus the result of Sweezy's calculations appears to be in line with
the formula I have given
above, namely,

P = TP· S,

which says that the total profits equals the total
surplus value if and only if TP = 1, i.e., if the
capital producing the goods the profits are spent on has an average
organic composition. (Since I
always set the total prices equal the total value, the above formula
says that both conditions --
the equality of the total prices and total value, and of total profit
and total surplus value -- are
satisfied if and only if TP = 1.) Moreover, by deriving this
result directly from the fact that a
certain sum of money may represent different values, depending on the
product it is spent on, I
have shown that this result has nothing to do with playing with
different monetary standards. Nor
does it have anything to do with other special features of the
Sweezy/Bortkiewicz calculations.

Funny money, or the search for the golden numeraire

The Sweezy/Bortkiewicz calculations are relatively complex, and
Sweezy's claims about what
they showed are rather obscure or even contradictory. So the thought
seems to have arisen that
he had satisfied the various helper formulas in the situation where the
luxury sector had an
average organic composition, and perhaps one could go further and
satisfy them all in more
general situations. This was particularly because Sweezy, following
Bortkiewicz's example,
brought into the calculations the issue of setting this or that
standard of money. In fact, the issue
of trying different "numeraires" (standard basis for measuring money or
value) introduces
numerous mind-numbing complexities into the argument, while obscuring
its essential features.
Yet, for some academic economists, finding the proper numeraire took on
something in the
nature of the search for the Holy Grail.

As I have shown above, the basic feature of value that explains the
modifications needed in the
helper formulas has nothing to do with what standard one takes for
money. Let's look at some
additional reasons why that's so. Consider the two products, A and B,
which were considered
earlier in this article, which have the same value but different
prices, A costing $100 and B
costing $200. If we change the numeraire for calculating prices, if the
standard of value is, say,
reduced in half, then A will cost $200 and B will cost $400. The prices
change, but the ratio of
these prices remains the same. Similarly, if one changes the numeraire
for values, the ratio of the
values of two products remains the same as it was before.

Now what is the issue in the transformation problem? Ultimately, it
is that A and B might have
the same value, but different prices. Or, more generally, given two
products X and Y, the ratio of
their values, valX/valy, differs from the ratio
of their prices of production, x/y. This is the
fundamental issue that gives rise to the need to modify the helper
formulas. But the change in
numeraires can have no effect on either valX/valy
or x/y. No matter how they change, it is always
going to be the case that

x/y = (Tx · valX) / (Ty· valy) = (Tx/Ty) (valX/valy).

So even though changing the numeraire may seem to make certain
formulas work right, it is
bound to do so at the expense of creating a problem elsewhere with
other formulas.

But when the numeraires are changed in the midst of calculations,
what is happening gets
obscured. It becomes easy to make such errors as inadvertently defining
the standard of money
twice, thus introducing inconsistency into the calculations.

The so-called "new solution"

The so-called "new solution" was developed in the 1980s by a number
of academic economists.
Its focus is in ensuring that certain formulas, such as that the total
profits equals the total surplus
value, be maintained without modification.(18) To do this, it makes use of two
methods.

On one hand, it searches for a new numeraire. But, as noted above,
this can't by itself suffice. So
on the other hand, the "new solution" redefines pricing for variable
capital, and -- in some
variants -- for constant capital. By having different pricing
mechanisms for different categories
of things, it can avoid the problem that setting a different numeraire
doesn't affect the ratio of the
prices of different things. So the "new solution" involved arguing that
its way of looking at the
prices and values of variable and constant capital is better than the
ordinary Marxist way.

Thus the "new solution" doesn't look into the significance of the
same sum of money
representing different values, the issue for which I have introduced
the L's (ratio of value
measured in labor-hours to price) and U's (ratio of value measured in
dollars to price), but
continues the old path to hell of seeking to brush them aside. As a
result, it has been subject to
the criticism, among other things, that "in the set of 'new solution'
prices of production the sum
of the values of constant capital does not equal the total sum of its
prices."(19) Of
course, from the
point of view of this article, the value of the total constant capital
C = UC· C, so it's clear why C,
the sum of the values of the constant capital, doesn't usually equal C,
the sum of the prices of
production of the constant capital. But for the "new solution", it's
would be a mystery why the
value and price of production of the total constant capital should
differ.

Altogether, the "new solution" is a complex system that is obscure,
arbitrary, and even differs
among its advocates on important points such as how to deal with
constant capital. One Marxist
category after another is reinterpreted, supposedly in the name of
Marx's real intention. It saves
one or two helper formulas by, in essence, sacrificing the content of
the Marxist theory of value.

Anwar Shaikh and the transfer between two circuits of capital

Anwar Shaikh has some useful contributions to the transformation
problem, such as his analysis
of the iterative method by which prices of production can arise from
values, which I hope to
discuss in a continuation of this article, but he has also sought to
explain the discrepancy
between total profits and total surplus value through the idea of
transfers taking place between
"the circuit of capital and the circuit of capitalist revenue".

In what Shaikh calls the circuit of capital, profit is reinvested to
form new capital, while in the
circuit of capitalist revenue, it is serves as "revenue", something to
be consumed by the
capitalists.(20) He
wrongly believes that it is the diversion of profit to revenue that
gives rise to
the possibility of the discrepancy between total profits and total
surplus-value.

Thus he holds that this discrepancy can't occur if all profits are
reinvested as capital. He writes
that this discrepancy "is the combined result of two factors. First, it
depends on the extent to
which the prices of capitalists' articles of consumption deviate from
the values of these articles. .
. And second, it depends on the extent to which this
surplus-value is consumed by capitalists as
revenue . . . Where all surplus-value is
consumed (as in simple reproduction), then the relative
deviation of actual profits from direct profits [surplus-value] will be
at its maximum. When, on
the other hand, all surplus-value is re-invested (as in
maximum expanded reproduction), then
there is no circuit of capitalist revenue and
consequently no transfer at all. Total actual profits
must, in this case, equal total direct profits,
regardless of the size and nature of individual price-value
deviations." (Emphasis added)(21)

By way of contrast, the formulas I have given above make no
distinction about whether the profit
is re-invested or consumed as revenue. Those formulas attribute the
discrepancy between total
profits and total surplus value entirely to the organic composition of
the goods represented by the
profits differing from the average organic composition. It makes no
difference whether the
profits are used to expand the means of production or as revenue: if
the organic compositions
differ, then there will be a deviation between the total profit and the
total surplus value.
Moreover, these formulas also say that there are no transfers in
physical or value terms among
the total constant capital, total variable capital, and total surplus
value (although there is a
redistribution of surplus value in physical and value terms among
individual capitalists): the
difference between total profits and total surplus value only reflects
different ways of measuring
the same amount of goods.

Shaikh didn't simply present a theoretical argument for his view of
the two circuits of capital,
but conscientiously sought to verify his argument about the transfer
between two circuits by
using a mathematical model of an economy and calculating the difference
between the total
surplus value and total profits. But the model he chose had some
special properties. It assumed
that the new investment in means of production and consumption was exactly proportional
to the already existing
means.

Shaikh points out that, in this model, when all the surplus value is
devoted to reinvestment, and
there is no revenue at all, then there is no deviation between total
profits and total surplus value.
And that's right, but not for the reason Shaikh says. It's not simply
because there isn't any
capitalist revenue. It's because, in his model, in the case where there
is no revenue (a) this model
would have only means of production and consumption, and (b) the goods purchased by the
profits would be
means of production and consumption in exact proportion to
the already existing means of production and consumption. So, for
example, if the economy grows 10%, then every constituent part of the
economy grows 10%: so,
in particular, the total constant capital grows 10%, and the total
variable capital grows 10%. In
this case, the surplus value, which consists solely of the added 10% in
means of production and consumption, has
the exact same organic composition as the economy as a whole. In this
case, TS = 1, and so total
profits and total surplus value would be equal.

But suppose, while still assuming that all the surplus value was
devoted to reinvestment,
Shaikh's assumption of proportional growth is dropped. Then, even
though all of the surplus
value was reinvested, if it was invested in an
assortment of means of
production and consumption that wasn't proportional to the already existing
means, then
there would be a total profits/total surplus value deviation by an
amount equal to the price-value
deviation of the new means of production and consumption coming from the surplus value.
I give an example of
this in appendix 2. This refutes the claim that the total profits/total
surplus value deviation can
only come from the use of profits as revenue. It shows that even
when there is no capitalist
revenue at all, and hence no "circuit of capitalist
revenue", the total surplus value can deviate
from the total profits.

Now, Shaikh used his model not just in the case when all profits
went to reinvestment, but also
when the profits were divided between reinvestment (which, in his
model, was to be strictly
proportional to the existing means of production and consumption) and capitalist
revenue. Shaikh obtained a
formula for the deviation between total surplus value and total profit
that only referred to the
revenue and not to the part of the surplus value that is
realized as means of production and consumption.

Nevertheless, in actuality, even in this case, the total deviation
between the surplus value and
profits comes from the sum of two deviations
-- that coming from the amount of profits devoted
to capitalist revenue (call this REV) and the amount of profits that is invested in expanding the means of
production and consumption (call this SMPC). True, Shaikh's formula doesn't refer
explicitly to SMPC. But with a
little algebraic manipulation of the formula, this can be seen as
follows:

To begin with, restating the results of Shaikh's model with the
symbols used in this article, he
obtained the result that P - S, the difference between the
total profits and the total surplus value,
was

Here, at first sight, the total profits/total surplus value
deviation depends only on the deviation
resulting from REV, the capitalist revenue. This seems to verify
Shaikh's view. But note that the
total profits/total surplus value deviation isn't equal
to the deviation between the price of
production and value of REV. It is, as Shaikh himself notes, only equal
to a fraction of it, to that
deviation divided by (1 + g). This means
they're unequal. This means that the total profits/total
surplus value deviation isn't composed simply of the price/value
deviation of the REV, but that
there is also another factor involved. And, with some minor algebra, we
can see that this other
factor involves the price/value deviation of the surplus means of
production and consumption, SMPC.

Let's see this in formulas. The total surplus value is composed of
capitalist revenue, plus the
surplus means of production: S = REV+SMP. And so the total profits
equals

P = REV + SMPC. Subtracting one from the
other, the result is

P-S = (REV-REV) + (SMPC - SMPC).

That is, the total profits/total surplus value deviation is the sum
of the price/value deviation of
the revenue and that of the surplus means of production and consumption.

Now, Shaikh obtained the result that

P-S = (REV -REV)/(1+g). This can be
rewritten as

REV - REV = (1+ g)(P - S).

And so

SMPC - SMPC = (P - S) - (REV -
REV) = (P - S) - (1+ g)(P - S)

= - g(P - S). Dividing both sides by -g,
the result is

P - S = - (SMPC - SMPC)/g.

Thus the total profits/total surplus value deviation can be
expressed by a formula that involves
only the surplus means of production and consumption, SMPC. Shaikh's formula for P-S
only involved the
capitalist revenue REV, but this formula for P-S only involves
SMPC. And both formulas are
right.

What's happening is that, in Shaikh's model of proportional growth, REV-REV
and SMPC-SMPC
aren't independent of each other. Instead, if you know the numerical
value of one of these terms,
you can calculate the numerical value of the other. In fact, REV
-REV = (1+g)(P - S) = - ((1 +
g)/g) (SMPC - SMPC).

This is not always true. Usually, knowing the numerical value of SMP
-SMP doesn't tell one the
value of REV-REV. But in the special economy that Shaikh
considered, it does. And therefore,
when considering this special economy, there is no significance to the
fact that one of the
formulas for P-S contains only REV and not SMPC. One can express
the total profits/total surplus
value deviation either in a formula containing only REV or in a formula
containing only SMPC,
as one chooses. The total profits/total surplus value deviation ­ in
the special case of
proportional growth ­ is proportional to the price/value deviation in
revenue, but it is also
proportional to the price/value deviation of the reinvested profits (surplus means of
production and consumption), so there isn't a special
role for revenue, not even in Shaikh's model.

The vagueness and indeterminacy of money

Above I have shown that the mathematical objections to the Marxist
transformation process can
be overcome by taking systematic account of the fact that the amount of
value represented by a
sum of money depends on what products are bought with it. This property
of value could be
described as a certain vagueness or indeterminacy of value: a sum of
money might represent any
of a range of values depending on what it is going to be spent on. On
the average a sum of
money -- provided one doesn't get cheated in the marketplace or cheat
others -- s a
definite value. So it appears that money should always have a definite
and precise value. And in
practice, for many economic problems, one can take it as always having
a certain value. But
when one looks closely, it turns out that a certain sum
of money can represent different values.

The idea that value has some inherent vague and indeterminate
features might be a shocking
concept to those who aren't familiar with it. The Marxist concept of
value is often misunderstood, as a result of which it is widely felt
that value can serve as a corrective to the ills of
financial transactions. Indeed, some left-wing trends see socialist
planning as planning in labor-hours.(23)
And a prominent left-wing economist has advocated that the Venezuelan
government
shift money in the direction of being denominated in labor-hours as the
way to deal with
inflation and move towards ending exploitation.(24) The idea that value can be somewhat
vague
and indeterminate goes sharply against this. But it seems to be widely
felt that to admit any
vagueness and indeterminacy in value is not to vindicate Marxist
economics and the labor theory
of value, but to undermine it.

Yet value is not a socialist alternative to financial calculation,
but a category that explains the
underlying laws of the marketplace and financial calculation. The
vagueness of value turns out to
be a reflection of the fact that money and financial calculation have a
similar vagueness. Indeed,
bourgeois economics has had its hands full trying to shove this back
under the rug, and seeks to
hide the indeterminacy of its calculations in obscure terminology and
complex mathematics.
Once one understands the vagueness and indeterminacy of money, it makes
it easier to
understand the properties of value and the Marxist view of the labor
theory of value. In contrast
to the bourgeois economists, Marx directly referred to value and price
as "non-natural"
properties of products.

Inflation

Common sense might at first seem to lead to the conclusion that if
an economic category, such as
value, has some vague and indeterminate features, then it must be a
mistaken category, a chimera
that doesn't really exist. So let's look at inflation. Surely no one
will deny that inflation is a real
phenomena, something that affects everyone. Even today, when
unemployment, speedup, and
wage-cutting are ever-more-terrible causes of growing insecurity and
mass misery, no one can
forget inflation in health care, education, and food costs either.

But how does one measure inflation? If there were only one product
on the market, it would be
easy. The cost-of-living index would simply track how far that product
increased or decreased in
price.

But there are many products on the market. They don't all change
their prices in the same way
and to the same amount. Some may even go down as others go up. The
cost-of-living index has
to be an "aggregate" index, that lumps together the different changes
that take place in the cost
of different products into a single, averaged-out figure. But one can't
just give equal weight to all
the products: a product that is rarely used shouldn't count as much as
something that one needs a
lot of. So one has to use a weighted average.

But different people buy different market-baskets of goods; people
use different goods in
different areas (and they are often priced differently in different
areas); and as goods become
more expensive, people shift from goods they can no longer afford to
cheaper ones. Does one
calculate a weighted average based on the assortment of goods people
bought in the earlier years,
or the later years? When things were cheaper or when things were more
expensive? All these
things, and more, cause problems in preparing the proper average for
the cost-of-living.

Perhaps the reader thinks that I am making a mountain out of a
molehill, and that really, for
crying out loud, all these complexities can be overcome. But take a
look at the New Palgrave
Dictionary of Economics, a massive reference work prepared by
eminent bourgeois
economists.(25) Its
entry on inflation states that "Since there are many different ways of
measuring prices, there are also many different measures of inflation."(26)

In other words, there is no one accepted way of defining inflation.
Thus vagueness and
indeterminacy creep into so basic and clear a concept as inflation. As
an example of this, even
after decades of preparing the Consumer Price Index, it continues to be
revised. Some of the
pressures to revise the CPI are political, as now when the ruling
bourgeoisie doesn't want to pay
cost-of-living raises to workers or Social Security recipients, and so
wants to minimize the cost-of-living index. But it's also true that
there are legitimate questions about how to maintain the
CPI.

Continuing with The New Palgrave on inflation: "The most
commonly used measures in the
modern world are the percentage rate of change in a country's Consumer
Price Index or in its
Gross National Product deflator." If one follows up on this by looking
at the entries for national
income, creating an index, inflation accounting, and similar topics,
one will find references to
more and more ambiguities in the concept of inflation, and to more and
more competing and
complicated mathematical formulas.

Despite these complexities, it's clear that not only is inflation a
real phenomenon, but it's
possible to prepare price indices that are good enough for many
practical purposes. This is true
for comparing prices over a relatively short period of time, and in an
economy whose overall
structure hasn't changed substantially during this period. But, and
this goes against common
sense intuition, one will need different price indices in different
situations, or even for measuring
different aspects of inflation in just one situation.

From the point of view of mechanical materialism, any category which
doesn't have a precise
value -- in principle, even if one only knows the value approximately
in practice -- is suspect.
But from the point of view of dialectical materialism, such categories
exist and are widespread.
Social behavior, such as marketplace behavior, is arbitrary and
indeterminate with regard to an
individual's decision, but has an iron logic of its own when a mass of
people take part. And such
things also take place in the physical world. In quantum mechanics,
categories such as position,
velocity, mass, energy and even time lose some of their precision and
become, in a sense, vague
and indeterminate except during times of "collapse of the wave
function", when they are
precisely measured. Ironically, it's only by taking account of this
indeterminacy that quantum
mechanics is able to achieve great precision in its calculations.

The index problem

The problem of creating a price index and defining inflation is a
special case of what's called the
"index problem" -- the problem of finding a single numerical figure
that represents the reality of
several qualitatively different things. One can easily measure the
increase or decrease of price of
a single product in a single market: it's when one has to construct an
index to keep track of all of
them combined, that the problem arises. And the index problem is
theoretically unsolvable. By
that I mean, one can construct indices that are useful within limits,
but one can't construct a
perfect index. If one needs precise enough information, one will end up
having to use many
indices, such as the inflation indices in different cities, or the
inflation for producer goods as
opposed to consumer goods, or -- as one sometimes sees in the newspaper
-- the figure for the
core inflation minus energy costs, etc.

This problem is not peculiar to inflation, but comes up in the
preparation of index numbers in
general. Take a look at the entry for "index numbers" in The New
Palgrave: it refers to a variety
of competing indices; goes on for fourteen pages; refers to the most
abstruse mathematics; and
includes a huge bibliography of over a page.(27) However voluminous the literature on
the
transformation problem may have been, the literature on the index
problem dwarfs it; however
obscure the material on the transformation problem may have been, the
index problem, as
discussed by bourgeois economics, reaches similar depths of obscurity;
and the index problem
will never go away, because while indices are necessary and useful for
certain purposes, there
never will be one perfect index, or perfect way of preparing indices,
good for all situations and
completely accurate. A single number (or scalar quantity) simply can't
reflect the full reality of
inflation, or productivity, or other economic categories. This isn't
simply because the
statisticians lack sufficient knowledge of the economy: it's because in
principle, even if the
statisticians knew everything, any single index they prepared could
only be approximately
accurate, and even that only within a limited range. Reality is
multi-dimensional; indices are
one-dimensional. The New Palgrave doesn't say in so many
words that the index problem is, in
principle, unsolvable, but that's what the huge length of the entry on
index numbers testifies to.

In practice, this problem comes up with respect to the most common
economic categories,
including measuring the size of the national economy, measuring
efficiency, and so forth. The
entries of The New Palgrave on these subjects describe
competing systems used for various
measurements or even refer directly back to the problem of index
numbers.

The aggregation problem

If measuring inflation is one aspect of the index problem, the index
problem in turn is one aspect
of the so-called aggregation problem, that of combining qualitatively
different things into a
single category. For example, such categories as "capital" or "consumer
goods" group together
many different products. When such aggregate categories are created,
there is generally an
attempt to measure them by adding together the cost of all their parts,
or by using some other
way to create an index.

The entry in The New Palgrave for the "aggregation
problem" raises the issue of whether such
overall concepts have a real meaning at all:

"Microeconomic theory elegantly treats the behaviour of optimizing
individual agents in a world
with an arbitrarily long list of individual commodities and prices.
However, the desire to analyse
the great aggregates of macroeconomics -- gross national product,
inflation, unemployment, and
so forth -- leads to theories that treat such aggregates directly. What
is the relation of such
theory (or empirical work) to the underlying theory of the individual
agent? When is it possible
to speak of 'food', rather than of 'apples, bananas, carrots, etc.'
When can one treat the
investment decisions of all firms together as though there were a
single good called 'capital' and
all firms were a single firm?

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

"Such results show that the analytic use of such aggregates as
'capital', 'output', 'labour' or
'investment' as though the production side of the economy could be
treated as a single firm is
without sound foundation. This has not discouraged macroeconomists from
continuing to work
in such terms."(28)

This discusses the aggregation problem from the standpoint of an
establishment economist who
is in love with bourgeois microeconomics.(29) It also displays the standpoint of
mechanical
materialism, according to which general categories such as "food",
"capital", and "investment"
aren't meaningful if they can't be handled as one-dimensional
mathematical entities.

The Cambridge capital controversy

A special case of the aggregation problem, the validity of the
concept of capital itself, was
debated in the so-called "Cambridge capital controversy". It is
referred to in a subsection of the
entry on "capital theory: debates" in The New Palgrave.
At one point, in discussing the neo-Ricardian Piero Sraffa's view of
the matter, it points out that he believed he had "destroy[ed] the
foundations of those versions of the traditional theory that attempted
to define the conditions of
production in terms of production functions with 'capital' as a factor.
Moreover, as regards the
concept of the 'capital endowment' of the economy conceived as a value
magnitude, the same
'real' capital may assume different values depending on the level of r
[rate of profit -- JG].
Sraffa concludes that these findings 'cannot be reconciled with any
notion of capital as a
measurable quantity independent of distribution and prices'".(30)

Thus Sraffa held that the usual aggregate measure of the total
capital was faulty, because its
numerical value would differ depending on the general rate of profit in
the economy and the
division of wealth between workers and capitalidoes sts. So in Sraffa's
view, any real measure of the
total capital in an economy was of a somewhat vague and indeterminate
nature (these were
probably not the terms he used) until the rate of profit and other
issues were specified.

Marx, the aggregation problem, and value as "non-natural"

It is one of the strong points of Marx's version of the labor theory
of value that, although he
didn't use the present-day terms of "index and aggregation problems",
he raised the basic issues
behind them. He did this via making the distinction between abstract
and concrete labor a key
point of the theory of value. Concrete labor is the labor of this or
that individual, performed at a
certain time and place, with a certain level of skill, and a certain
intensity. By way of contrast,
abstract labor is human labor in general, an aggregate category that
encompasses the individual
labor of different individuals, in different branches of industry,
performed in different locations,
and with different levels of skill. One hour of concrete labor is
different qualitatively from
another, and produces a product which is qualitatively different from
that produced by another
hour. Such hours are not interchangeable: a particular type of labor is
needed for a particular
purpose. But abstract labor-hours are identical and interchangeable:
one can be exchanged for
another, and in fact is so exchanged in the form of money.

Marx pointed out that the marketplace, by equating concrete labors,
turns them into abstract
labor, and strips them of their particular properties. He wrote in Capital
that

". . . As use-values, commodities are, above all, of
different qualities, but as exchange values
they are merely different quantities, and consequently do not contain
an atom of use-value.

"If then we leave out of consideration the use-value of commodities,
they have only one
common property left, that of being products of labour. But even the
product of labour itself has
undergone a change in our hands. If we make abstraction from its
use-value, we make abstraction at the same time from the material
elements and shapes that make the product a use-value;
we see in it no longer a table, a house, yarn, or any other useful
thing. Its existence as a material
thing is put of out sight. . . . there is nothing left but what is
common to them all; all are reduced
to one and the same sort of labour, human labour in the abstract."(31)

Marx pointed out that abstract labor has a purely social existence:
it is not a material entity, but
is created by marketplace exchange. He pointed out that when, by
exchange, one equates, say, a
certain quantity of iron to a certain quantity of sugar-loaf, the
result "represents a non-natural
property of both, something purely social, namely, their value."(32)

Thus measuring things in abstract labor, or aggregating a group of
things by adding together
their cost (the quantity of abstract labor they contain), eliminates
the specific nature of things.
Thus the total cost, the financial index, is not a "natural" property
of things, and it obscures the
qualitative features of things that must be taken account in natural
planning. Neither price nor
value are natural properties of material objects, but social
properties, in particular, marketplace
properties. Marx referred to the difference between planning taking
account of qualitative
differences on one hand and marketplace exchange via abstract labor
(money) on the other, as
follows:

"...Thus, economy of time, along with the planned distribution of
labour time among the various
branches of production, remains the first economic law on the basis of
communal production
[production in a classless and moneyless society -- JG]. . . . However,
this is essentially
different from a measurement of exchange values (labour or products) by
labour time. The
labour of individuals in the same branch of work,
and the various kinds of work, are different
from one another not only quantitatively but also qualitatively. What
does a solely quantitative
difference between things presuppose? The identity of their qualities.
Hence, the quantitative
measure of labours presupposes the equivalence, the identity of their
quality."(33)

So Marx saw that measuring things according to a
single index (which is the same as seeing
nothing but the quantitative difference between things) results in
slurring over and overlooking
their qualitative differences. This is a clearer and more general
presentation of the index and
aggregation problems than is common in present-day economics.

A social and non-natural category is still a real category

Marx elaborated on the social character of value in his famous
analysis of commodity fetishism.
He pointed out that price and value represent social relationships
between people disguised
as relations between objects. This is important because if value were a
relationship between
objects, it would be something eternal, something that will exist so
long as humanity needs to
deal with material objects. But if value is a relationship between
people, then its role will last
only so far as the particular social conditions giving rise to this
relationship, namely marketplace
relationships, exist.

But Marx, as a dialectical rather than mechanical materialist,
didn't write off social relationships
as something that didn't really exist. The fact that money and value
represent social relationships
and that they are non-natural doesn't meant that they are arbitrary
categories or fraudulent ones
(although fraud does play a big role in the accumulation of many
capitals). Marxism doesn't hold
that abstract labor, though subject to the aggregation problem (the
blurring of qualitative
properties), doesn't exist. On the contrary, the goal of capitalist
production is to produce surplus
value and increase capital. The fact that value and capital are subject
to the index and
aggregation problems doesn't destroy their use as categories for
certain purposes: on the
contrary, it's the strong point of Marxist economics that it points out
the key role that these
aggregate quantities play in capitalism, and it's the rule of these
aggregate quantities that is the
law of value, the law of the devastation of the working class and of
the environment. Marx both
pointed to the central role of these aggregate quantities, and analyzed
their particular nature, the
particular contradictions that were inherent in them.

Money illusion and value

But for most of those working on the transformation problem, value
was implicitly a natural --
almost a material -- category. The modification of the helper formulas
requires explicitly
dealing with a certain indeterminacy of value, and this goes against
the strong feeling that the
value of a sum of money should be as well-defined as the mass of a
particle.

The New Palgrave has an entry on what it calls "money
illusion": "The term money illusion is
commonly used to describe any failure to distinguish monetary from real
magnitudes. It seems to
have been coined by Irving Fisher, who defined it as 'failure to
perceive that the dollars, or any
other unit of money, expands or shrinks in value'. . ."(34)

But the widespread money illusion in capitalist society goes way
beyond simply forgetting at
times to correct prices for inflation. It's the belief that monetary
indices have a real, essentially
physical meaning. Bourgeois economics restricts the idea of "money
illusion" to some
technicalities, while promoting money illusion overall. For example,
take the work of William
Nordhaus, an eminent neo-liberal economist working on environmental
models. He's confident
that he can evaluate the costs and benefits of environment action for
decades in advance via
setting discount rates and elasticities in a financial spreadsheet. It
never strikes him that financial
indices are impotent with respect to major changes in the
infrastructure and the environment.
Money illusion has reached the point where bourgeois economists think
that financial fantasy
can make up for their lack of knowledge about future technology as well
as the limits of our
knowledge about how the global climate works.(35)

But money illusion doesn't exist only among the neo-liberals. It
gets carried over into the
transformation problem in the belief that value, which is simply the
essence of pricing, has such
a meaning.

Living under capitalism, we have to buy and sell all the time. We
need to be vigilant to buy and
sell things at their value: we don't want to be cheated, and we don't
want to cheat other workers
who we may be dealing with. The idea that commodities have a definite
and proper value is
beaten into us 24/7, by everyday practice. And this suggests that
things would be fine if only
everything, our labor as well as the things we buy, were bought and
sold at their proper value.

But Marxist economics says otherwise. The law of buying and selling
things at their value is the
law of enslaving people to the marketplace; it is the law of an
obsolete economic system that
must be replaced by something new. Thus true Marxist economics uses
value to show the
contradictions of capitalism and money, not as a model of what prices
should be to have good
things happen. From this point of view, it is not surprising that if
money is subject to the index
and aggregation problems, then these contradictions should be reflected
in value as well.

The transformation problem is in essence a form of the aggregation
problem: the simple formulas
for value work properly if all spheres of production have the same
organic content, but one has
to aggregate with spheres of other organic content. And I have shown
that the modifications
needed to the helper formulas involve recognizing that a sum of money
has an indefinite value
unless the products which will be bought with it are specified. This in
turn is a reflection of the
fact that the aggregation and index problems show that money has
indefinite and indeterminate
features. It is a reflection of a certain vagueness and indeterminacy
of money, as well as of
value, that a sum of money has an indefinite value until the products
which will be bought with it
are specified.

True-value pricing and the non-natural nature of value

At one time the idea that pricing things at their true value would
liberate the working class was
common. Today the idea of true cost pricing is promoted most often with
respect to the
environment. The idea is that if only carbon fuels were priced at their
true cost, then marketplace
forces would take care of restricting their use and providing for
alternatives.

Marx's idea was quite different. He held that it was the lack of
overall economic planning that
resulted in the devastation of the environment. He didn't look to a
reformed marketplace as the
way to deal with either environmental devastation or working-class
misery, but to conscious
planning by a humanity which was liberated from the marketplace and
from the private
ownership of the means of production.(36)

The aggregation and index problems strongly suggest that prices, no
matter how they are
adjusted, can't deal with the environment. An aggregate index, such as
price, slurs over the
particular features of each individual thing that it is supposed to
measure. If a price measures the
amount of carbon emissions, then it can't also measure the
socially-necessary labor needed to
produce a product. If it tries to measure both, then it is subject to
the aggregation problem, and it
can't really measure either adequately. This is not the only reason why
relying on market
measures to solve environmental issues won't work; it might not even be
the most important
reason; but it does help undermine as "money illusion" and commodity
fetishism the search for
the "true prices" that will supposedly result in marketplace forces
respecting the environment.

Marx and Engels analyzed the contradictions in value, and showed how
the law of value leads to
class exploitation and environmental devastation. But the widespread
misunderstanding of value
that existed in Marx's day and still today, is that value overcomes the
contradictions of
capitalism, and that the marketplace has contradictions because it
departs from value. From that
point of view, the idea that value could be vague and indeterminate in
any sense seems like a
slap in the face to the honor of value, a denial of its importance for
analyzing the capitalist
economy. But from the Marxist point of view, it means that value
accurately reflects the
contradictions inherent in money and marketplace exchange.

Appendix 1: List of abbreviations and formulas

(roughly in order of appearance)

val stands for value, the socially-necessary amount
of labor to make a product or, as the case
may be, to make the total amount of products in some sector of
production.

c stands for "constant capital", that is, capital
invested in other things than immediate,
productive, living labor. This is the material means of production,
such as raw materials, machinery, buildings, etc. However, the constant
capital is divided into two parts: circulating
constant capital and fixed capital.
Depending on context, in this article and in Marx's Capital,
c can mean either circulating constant capital or the total constant
capital.

r stands for the part of capital that is invested
in goods that are completely used up in the
production cycle, the circulating constant capital. I'll call it r
because raw materials are one
example of it.

Fixed capital is the part of the constant capital
that isn't completely used up during a production
cycle, such as machinery, buildings, etc. These things usually
deteriorate somewhat in a single
cycle. So the value of the fixed capital has two parts: the amount that
has worn out in a
production cycle and thus passed its value to the product, and the part
that remains unchanged,
the "persistent fixed capital".

w is the part of the fixed capital that gets
worn-out in a single cycle ­ -- the part of the machinery,
buildings etc that gets worn out.

f is the persistent fixed capital,
the part of fixed capital that isn't used up during a production
cycle. Note that most formulas that include f have to take account of
the entire production of a
commodity during a single production cycle.

w + r is the part of the constant capital used up
during a production cycle.

v + s represents the socially-necessary hours of
labor by the workers during a production cycle.

v represents the variable capital, which is used to
pay wages.

s represents the surplus-value.

s/v is the rate of surplus-value (rate of
exploitation).

R = s/(f + c + v) is the rate of profit. When one
considers f, the formula has to be calculated not
over an individual product, but for all the products during a single
production cycle.

s/(c + v) is sometimes given as the formula for the
rate of profit. This could be because f is taken
to be zero, for simplicity, when the fixed capital isn't relevant to
the problem under discussion.
Or it could be because c is taken to include f.

c/v is the ratio of the constant to the variable
capital, the so-called organic composition of
capital. When all technicalities are taken into consideration, there
are three slightly different
definitions of the organic composition of capital. (1) There is c/v,
with c and v measured in
value. (2) There is c/v, with c
and v measured according to prices of production. And there is
(3)
the "full organic composition", which takes account of
the organic composition of the branches
of industry that produce the goods (machinery, raw materials, etc.)
representing the constant
capital, and of the consumer goods representing the variable capital.

k = c + v is the "cost-price" of producing some
good; it is the capital actually expended; it does
not include the persistent fixed capital.

pp = k + R(f + k) = (c + v) + R(f + c + v) = Rf +
(1 + R)(c + v) is the price of production of
some good. If one sets f = 0 for simplicity, it is just k + Rk = (1 +
R)(c + v). But if one takes
account of f, it has to be calculated over an entire production cycle.
Or, alternatively, to apply the
formula to an individual unit of a commodity, one uses f=(value
of fixed capital)/N, where N is
the number of units produced by the machine in the course of a
production cycle. Finally, note
that the formula for pp is only approximate, as the exact equation of
this form would need to
have every category , including the rate of profit,
calculated according to prices of
production.

Category - When categories are underlined,
it always indicates that they should calculated via
prices of production, not values. For example, c represents the value
of the constant capital,
while c represents how much the constant capital would cost at
prices of production.

pp = (1 + R )k = (1 + R)(c
+ v) This is the revised formula for the prices of
production (when it
is assumed there isn't any persistent fixed capital). Since prices of
production appear on both
sides of the equation, it expresses a relationship among prices of
production rather than giving an
explicit definition of how to obtain prices of production from values.

R is the rate of profit calculated via
prices of production. Marx implicitly held that the rate of
profit is the same whether calculated in value terms or prices of
production. However, as is
pointed out in the rticle, the rate of profit R does differ somewhat
when calculated in value
terms or in terms of prices of production.

Marx's helper formulas for the transformation
process are given later in this list, just before the
modified helper formulas

A and B are taken here to be two
different commodities or products which have the same value,
of five labor-hours, but B sells for twice the price as A, a single A
selling for $100, and a single
B for $200.

An economic category, such as c or v or s, may be measured in
three-different ways in this
article. When it is important to make such distinctions, they will be
indicated as follows:

Category is the category measured in value terms,
but the value is expressed in dollars, with one
labor-hour represented by the average amount of money that a product
with the value of one
labor hour costs, averaged over the entire economy.

Categorylh is a category as measured in
hours. It is the amount of socially-necessary labor-hours
represented by the commodities in that category. It is a category
measured not only in value, but
with the value measured directly in labor-hours.

Category is, as mentioned above, the
category measured in prices of production.

m is an amount of money, usually used for how much
something costs. m usually is the price if
things were priced at their value, and m if
things are priced at the price of production.

L=Laverage=Lall, standing for
labor-hours, is the average ratio between labor-hours and dollars; it
is the amount of abstract labor-hours contained in a product worth one
dollar, averaging over all
the products in the economy. Alternatively, when everything is
bought and sold at its value,
it is the amount of abstract labor-hours contained in any
product that costs one dollar.

D=Daverage=Dall, standing for
dollars, is the average ratio between dollars and labor-hours; it is
also the cost in money of the product of one labor-hour, in dollars per
abstract labor-hour, when
everything is bought and sold at its value.

L = 1/D, and D= 1/L.

vallh = L · m.

m = D · vallh
.

When things are bought and sold at their prices of productions,
these formulas with L and D
break up into many formulas, each with its own separate L and D (such
as LA or DB) since these
ratios vary for different products. For example,

vallh = Lproduct · m
or, more explicitly, valproductlh = Lproduct
· mproduct where separate formulas have to
be written for each product, thus:

vallh = LA · m or,
more explicitly, valAlh = LA · mA

vallh = LB · m or,
more explicitly, valBlh = LB · mB.

More generally, if one is considering the total or aggregate values
and dollar sums for a basket of
several products, A,B,C,etc., one has

val = Dshopping basket · vallh
where Dshopping basket is averaged over the various products
in the shopping
basket.

U, or more explicitly, Uproduct, is the ratio between the
value, measured in dollars, to the value
of the product. Recall Lproduct is the amount of value, measured
in labor-hours, represented by
one dollar's worth of that product. The difference between the U's and
the L's is that value is
measured in dollars as far as U is concerned, not labor-hours. Wait,
someone may say, wouldn't
the amount of value, represented in dollars, of one dollar always be
one dollar?! No! The point is
that, once one switches to prices of production, the amount of value
represented by a specific
product that costs one dollar changes, depending on the organic
composition of the capital
producing that product. When one measures value in dollars, one
represents a labor-hour by the
average amount of dollars that a labor-hour
represents, averaged over all products. By
way of
contrast, Uproduct represents the value, measured by the
average amount of dollars a labor-hour
represents, of a dollar's worth of a specific
product. Thus, how far Uproduct differs from 1
represents the deviation between price and value introduced by prices
of production, while Uentire
output =1.

val = UX *m or, to be more
explicit, valX = UX *mX
.

TX is the ratio between the price of
production of a product, and its value, measured in dollars.
Once again, this might at first blush seem to always be 1 by
definition, but read the comment on
why the U's aren't always equal to 1. T (for transformation)
is used for this ratio because the
transformation problem was first formulated as finding the price of
production of a product of a
certain value. The price of a product, when things are bought or sought
at their value, is mX=valX.
And the price of production is mX = TX
·valX =TX · mX. So the traditional
transformation problem corresponds to calculating the T's.

m = TX · val.

TX = 1/UX.

UX = 1/TX.

Tall=Taverage =1 as this
article sets the total prices of production equal to the total values.
But TA
varies depending on the organic composition of the capital used to
produce A's. TA is less than
one when A is produced in a labor-intensive sphere of production, and
greater than one in the
capital-intensive situation.

Similarly, Uall = Utotal product = Uaverage
=1 but the UA's vary depending on the organic
composition
of the capital used to produce A's. However, UA is greater
than one when A is produced in a
labor-intensive sphere of production, and less than one in the
capital-intensive situation.

The simple three-sector model of an economy
undergoing simple reproduction (i.e., a omy) involves means of production, means of consumption, and the
luxury sector, with
capitalist profits, and only capitalist profits, used to buy the luxury
goods.

Ttotal profits does not
necessarily equal 1 in the three-sector model, unless the organic
composition of the luxury sector is the
same as the overall organic composition of the economy.

Capitalized categories -- in general indicate
categories that that refer to the entire economy or
to large branches of it: for example, c is the constant circulating
capital used in producing a
product, or a collection of products, while C represents the entire
constant circulating capital of
the economy.

S is the total surplus value generated in one
economic cycle of the entire economy, measured in
dollars.

P is the total profits produced in the
entire economy. In the economic models used in discussing the
transformation problem, the total surplus
value and the
total profit refers to the same physical amount of goods (this is not
true for the surplus value and
profits obtained by any one capitalist); however, the surplus value
represents the total value of
these goods, while the profits refer to the total of the prices of
production of these goods. So P
and S, the total profits and the prices of production of the
goods representing the surplus value,
are the exact same thing: P = S.

P = Ttotal profits · P = Ttotal
profits · S.

C is the total constant capital for the entire
economy.

V is the total variable capital of the entire
economy.

E is the total size of the output of one production
cycle, and equals C + V + S. Since the total of
the prices of production equals the total value, E = E.

Marx's view was that the equalization of the rate of profit resulted
in the total surplus value
remaining the same (but being redistributed among individual
capitalists in a different way).
That is so, as expressed in both value and physical terms. It is not
exactly so when measured by
prices of production (except in the special case when Utotal
profits = 1).

Revenue is the part of the total production of the
economy that goes into consumption, rather
than replacing or expanding the means of production.

Capitalist revenue is the part of the surplus value
that goes for the capitalists' personal
consumption rather than being reinvested in expanding the means of
production.

REV stand for the capitalist revenue for the entire
economy

SMPC stands for the part of the surplus value that
is realized as means of production and consumption and can be
used for expanding the scale of production.

REV - REV is the deviation
of the prices of production of the total capitalist revenue from the
value.

SMPC - SMPC is the deviation
from its value of the price of production of the part of the surplus
value that is realized as means of production and consumption.

g is the growth rate from one economic cycle to
another in Anwar Shaikh's economic model of
proportional growth referred to in the text.

Appendix 2: A counterexample to Shaikh's view of the transfer
between two circuits of
capital

Earlier, in the section "Anwar Shaikh and the transfer between two
circuits of capital", I
discussed his view that the discrepancy between total profits and total
surplus value occurs
because of transfers taking place between "the circuit of capital and
the circuit of capitalist
revenue". I showed that, despite his other contributions to the
discussion of the transformation
problem, this particular conclusion is mistaken. But it might also help
those who are somewhat
familiar with economic models to see a concrete example of how
disproportion can result even
without a "circuit of capitalist revenue".

This can seen by using a model of a very simple two-sector economy
that has only means of
production (the material form of constant capital) and consumer goods
(the material form of
variable capital); there are no capitalist luxury goods at all, and all
profit is ploughed back into
increasing production. Let's also assume that the rate of exploitation
is 100%, so that the v = s
(i.e., there is as much surplus value as variable capital expended on
wages). In the sector devoted
to means of production, let's say that it uses 3 units of means of
production for every unit of
variable capital. Let's measure in units of millions of
dollars to make it be a respectable
production cycle of a small economy. Then we might find that the value
of the means of
production that are produced in the first production cycle is 500:

With respect to variable capital, let's assume that the consumer
goods which the variable capital
is spent on are produced by a process that uses 1 unit of means of
production for every unit of
variable capital. Then we might find that the value of the means of
consumption produced in one
production cycle is 300:

This works out quite well, as 500 units of means of production are
produced in a production
cycle, 400 of which replace the used up means of production (300 units
of means of production
used up in producing means of production, and 100 units used up in
producing consumption
good), leaving 100 units of surplus product (which is the material form
of the surplus value
which has been produced in this sector). Similarly 300 units of
consumption goods are produced
in a year, 200 units of which go to replace the used up consumer goods
(100 used up in producing means of production, and 100 used up in
producing consumer goods), and 100 are left as
surplus product.

However, the organic composition of these sectors differs
dramatically, with the sector
producing means of production having an organic composition of 300/100
= 3, while the sector
producing means of consumption has an organic composition of 100/100 =
1. And when
everything in priced according to value, the rate of profit differs in
these two sector, with the
sector producing means of production having a profit rate of
100/(300+100)=1/4 or 25%
(assuming that there is no fixed capital to worry about, so that the
rate of profit is just S/(C +
V)), and the profit rate for the other sector being 100/(100+100) = ½
or 50%. The overall rate of
profit for this simple economy is 200/(400 + 200) = 1/3, or
approximately 33.3%

In the next production cycle, something has to be done with the
left-over product. I'll specify a
particular way of doing this. Let production of consumer goods be
expanded, using 200 units of
means of production and 200 units of variable capital, instead of 100
units of each. But let the
production of means of production stay the same.

So there is the following chart for the second cycle of production:

Used up C

Used up V

S

VAL

rate of profit

leftover product

C

300

100

100

500

1/4

0

V

200

200

200

600

1/2

300

This works, as in the means of production sector, the 300 units of
means of production needed
for carrying on production have been created in the last cycle (which
produced a total of 500
units of means of production). And the 100 units of consumer goods
needed to carry on
production are available out of the 300 units of consumer goods created
in the last cycle.
Similarly, with regard to the sector producing consumption goods, it
requires 200 units of means
of production to in order to carry on, and that is available from the
means of production
produced in the last cycle since 500 means of production were produced,
and only 300 units are
needed by the means of production sector. And 200 units of consumer
goods are needed, and this
is available because of the 300 units of consumer goods produced in the
last cycle, only 100 are
needed in the means of production sector.

But production can't be expanded in the same way in the next, third
cycle, as there are no surplus
means of production created in the second cycle, and such a surplus
would be needed to support
further growth. I'll come back to this point later on. But first let's
check what happens when one
switches over from calculating in value terms and goes over to
calculations in prices of
production. I calculated the prices of production using the iterative
method which I hope to
discuss in a future continuation of this article. This method has been
championed by Shaikh and
others; it gives proper prices of production; and, for simple models
such as the above one, it is
easy to set up on a spreadsheet. I won't describe the method or my
spreadsheet here, but simply
give my results, which are verified by the fact that redoing the charts
with these prices show that
the rate of profit is indeed equalized in both sectors.

The results for the first cycle of production are as follows: the
price of production for a quantity
of the means of production is approximately 1.0871
times its value (TC=1.0871), while the price
of production of a quantity of consumption goods would be
approximately .8548 times the value
(TV =0.8548). Thus the price of production of goods in the
sector with the higher organic
composition goes up, and the price of production in the sector with the
lower organic
composition goes down, as expected.

Now to redo the chart for the first cycle in terms of prices of
production, one has to make the
following changes:

noting that the physical quantities of means of production used in
producing things doesn't
change in redoing the chart, only their price (which goes from values
to prices of production),
one multiplies everything in the "C" column by TC;

one multiplies everything in the "V" column by TV;

the "VAL" column becomes the "PP" (price of production) column,
and the entry in the "C"
row is multiplied by TC and the entry in the "V" row by TV;

the "S" (surplus value) column becomes the "P" profit column, and
the profit is calculated via
PP-C-V, where one takes the figure for the constant capital from the
first column, for the
variable capital from the second column, and the price of production
from the fourth column;

the rate of profit is calculated by P/(C+V); and

the "surplus product" for C is calculated by subtracting the sum
of the entries in the C column
from the entry in the PP column for the C row, and the entry for V
comes from subtracting the
sum of V column from the entry in the PP column for the V row.

The result is as follows:

C

V

P

PP

rate of profit

leftover product

C

326.13

85.48

131.94

543.56

.3206 (32.06%)

108.71

V

108.71

85.48

62.25

256.44

.3206 (32.06%)

85.48

And the overall rate of profit is calculated by dividing the total
profit (131.94+62.25) by the sum
of the total constant (326.13+108.71) and total variable (85.48+85.48)
capital. It comes out at
32.06%, which is not surprising, as the two sectors of production both
have the same 32.06%
rate of profit.

This chart represents the exact same amount of production in the
first cycle as before, and the
use of the exact same amount of means of production and consumer goods,
but they are
expressed in prices of production rather than value. With these prices,
one sees that the rate of
profit has been equalized at 32.06%. This verifies that these prices
are indeed the correct prices
of production.

But the total surplus value used to be 100 + 100 = 200 units, while
the total profit is now 131.94
+ 62.25 = 194.19 units. Thus there is now a discrepancy between total
surplus value and total
profits. It isn't very big, being merely 5.81 out of a total surplus
value of 200 units. But that's not
too surprising as these discrepancies usually aren't very big.
Nevertheless this is indeed a real
discrepancy; and it exists despite all the profits from the first cycle
of production being used to
expand production in the next cycle. This discrepancy thus has nothing
whatsoever to do with
the "cycle of capitalist revenue", which doesn't exist in this economy.
So this is the promised
counterexample.

Now let's look at some features of this example. Considering the
tremendous difference in the
organic composition of the two sectors, the prices of production don't
differ that much from the
values. The biggest deviation is for consumption goods, and that is
only 15%. This would seem
to be in line with prices of production being perturbations
(small corrections) from
values. Moreover, the overall rate of profit calculated in value terms
and in prices of production
is rather stable: it doesn't change that much, going from 33.3% to 32%.
The rate of profit for
each sector is adjusted, but the overall rate of profit stays pretty
stable. Of course a single
example such as this can only be suggestive of a general result, not a
proof.

It's useful to also redo the chart for the second cycle in prices of
production. It then looks like
this:

C

V

P

PP

rate of profit

leftover product

C

339.58

89.00

137.38

565.97

.3206 (32.06%)

0

V

226.39

178.01

129.63

534.03

.3206 (32.06%)

267.01

So here again we see that the total profits (89.00+178.01 = 267.01)
differs from the total surplus
value (200+100=300, as taken from the chart above of the second cycle
in value terms).

It's also notable that the prices of production change when they are
calculated for the second
production cycle. The price of production of the means of production is
now 1.132 times the
value (T = 1.132), and the price of production of consumer goods is .8900
times the value (T =
.8900). This is different from the first cycle. Why do the prices of
production change from cycle
to cycle in this example? Is this surprising? Not really. This is
because the relative sizes of the
two sectors have changed, due to the expanded production. The change in
the redistribution of
surplus value from one sector to another comes from a difference in the
organic composition of
the two sectors, but the influence that the different organic
compositions exercise is affected by
the size of the sector with that organic composition.

However, as mentioned above, it turns out that in the second cycle
there are no surplus means of
production available for expanding production further in the next
cycle. This means that one
can't simply proceed to a third cycle by repeating the transition from
the first to the second
cycle, i.e. leaving everything unchanged except increasing the
production of consumer goods
again, as that would require more means of production. So the only way
the third cycle could
absorb the surplus consumer goods is if there is some additional
change: a change in the organic
composition of the various sectors (due perhaps to technical change);
some reason to store the
left-over consumer goods, such as building up needed stockpiles; an
increase in wages; or some
other change. Otherwise the left-over consumer goods mean that the
second cycle results in an
unbalanced situation, where the excess of consumer goods may cause
price changes and a slow-down of production in the third cycle.

Does this mean that the example I have given of the first cycle is
unrealistic? No, not at all. It is
a general property of expanded growth that, unless this growth is
exactly proportional, it will
eventually give rise to an unbalanced situation -- unless
these disproportions are counteracted
by changes in the organic composition of the sectors or other factors.
For that matter,
proportional growth itself can be upset by changes in the organic
composition of the sectors,
running out of sufficient labor power or resources, etc. Growth and
change -- technical change,
change in markets, change in the availability of resources or labor,
and so forth -- give rise
repeatedly to disproportionalities. So it would be unreasonable to
assume that proportional
growth is the only case of expanded reproduction that has to be
considered. And in fact, Marx
does not assume proportional growth in his discussion of expanded
reproduction in Capital(39),
nor do various other studies of expanded reproduction. []

Notes

(1)The
value due to the labor embodied in the raw materials goes fully into
the value of the
product, whereas the value of the "fixed capital" such as machinery and
buildings only passes
gradually into the product as the fixed capital is used up.

(2)"Circulating"
capital is that part of the capital which is used up in a production
cycle, and so
must be replaced in order to carry on the next production cycle. This
includes both the capital
represented by materials which are used up in the course of production,
such as raw materials,
and that used to pay workers' wages.

(3)More
accurately, the surplus value is divided between that portion retained
by the capitalists as
their profit, and that part which is transferred to other exploiters,
or to the use of the capitalist
state, as rent, interest, and taxes.

(4)One
usually sees another formula here, just s/(c+v), not s/(f+c+v). That's
because, for many
purposes, what Marx calls the "persistent fixed capital" is just a
complication and can be left out
in order to simplify the discussion. Moreover, when the persistent
fixed capital is important,
small c may be used to mean the full constant capital, which in this
article is instead specified as
c + f. In Capital, c is used both ways, depending on context.
However, because in economic
crises like the ongoing depression, the depreciation of fixed capital
becomes a major issue, it's
useful to make the point explicitly that f is not
involved in the value of a product, but is
involved
in calculating the rate of profit.

(5)This
doesn't mean that a capitalist can make more profit by hiring more
workers than are
needed to do the job. These formulas assume that the workers work at
the average, or socially-necessary, rate of intensity, and only the
necessary labor is employed. The value of a product
doesn't go up because excessive amounts of labor are used, and yet that
extra labor has to be
paid.

(6)It might
seem natural that a ratio involving the amount of living labor is
called the "organic"
composition of capital. But it might then be natural to think that a
high organic composition
should be "labor-intensive", when in fact it is "capital-intensive". I
don't know why Marx
defined it in this way. Well, "organic" can mean something fundamental,
rather than something
living. And a fundamental of capitalist domination of labor is
capitalist ownership of the means
of production and other constant capital. From that point of view, a
high organic composition of
capital would correspond to more and more constant capital per worker.
I mention this sheer
speculation on how the "organic composition" got named only in order to
help the reader
remember more easily what is a high organic composition, and what a low
one.

(7)Ch. IX:
"Formation of a General Rate of Profit (Average Rate of Profit) and
Transformation of
the Values of Commodities into Prices of production" in Part II:
"Conversion of Profit into
Average Profit", Capital, vol. III, pp. 164-5, Progress
Publishers, emphasis as in the original.

(8)Marx
didn't use separate symbols to indicate whether he was evaluating
something in terms of
value or price of production. Instead, in certain passages on the
transformation problem, where
he thought the distinction had to be borne in mind, he would raise it
explicitly.

(9)It
should be remembered that in such examples it is assumed for simplicity
that products are
selling at the prices of production. One leaves aside cheating and
other ways of one buyer or
seller getting the best of another, as well as such issues as scarcity
or oversupply, that affect the
price offered everyone.

(10)These
models also specify that the technique of production remains the same,
and a
commodity still requires the same physical amount of raw materials, the
same amount of labor,
etc., to produce. As a result, in these models the value of a given
physical amount of goods
remains the same after the transformation to prices of production. So
both the total physical
amount of the goods bought by the profits, and the total value, remain
the same.

(11)Similarly,
the total surplus value is the same as the total profits when things
are priced at their
value. So S=P.

(12)Recall
that the physical goods represented by the total surplus value and the
total profits are
the same, so Ttotal surplus value is the same as Ttotal
profits.

(13)Recall
that in my calculations in this article, I always take the total of the
prices of production
to be equal to the total values. This amounts to using this equation to
set the standard of money.
Sweezy, however, spends a good deal of attention on setting this or
that standard for money.

After setting the total of prices to the total values, I then
investigate whether the other helper
formulas are satisfied, such as whether the total profits equals the
total surplus value. Sweezy, by
way of contrast, sets the total profits equal to the total surplus
value, and then checks to see
whether total prices end up equal to the total values.

(19)E.K.Hunt
and Mark Glick, "Transformation Problem", p. 361, in The New
Palgrave: Marxian
Economics, edited by John Eatwell, Murray Milgate, and Peter
Newman. This article contains,
among other things, a brief explanation and characterization of the
"new solution".

(20)Revenue
is the part of the total production of the economy that goes into
consumption,
whether workers' or capitalists' consumption, rather than replacing or
expanding the means of
production. Hence the "capitalist revenue" is the part of the profit
that goes for the capitalists'
personal consumption rather than being reinvested in expanding the
means of production.

(23)See
the three-part series "Labor-money and socialist planning" in Communist
Voice for a
refutation of the idea of labor-money or of the labor-hour being a
natural unit of socialist
calculation. (www.communistvoice.org/00LaborHour.html).

(25)The
New Palgrave: a Dictionary of Economics, 1987, first edition,
edited by John Eatwell,
Murray Milgate, Peter Newman. The second edition appeared in 2008, but
I don't have access to
it. The New Palgrave: Marxian Economics, referred to earlier
in this article, is one of a series of
volumes that consisted of reprints of those of the articles that bore
on a certain subject. The
introduction of that volume grandly proclaimed that The New
Palgrave "is the modern successor
to the excellent Dictionary of Political Economy edited by
R.H. Inglis Palgrave and published in
three volumes in 1894, 1896 and 1899. A second and slightly modified
version, edited by Henry
Higgs, appeared during the mid-1920s." It also pointed out that the
authors of the various entries
had their own, differing views. Although it asked its contributors to
be fair-minded, it didn't try
to suppress the differences among them. Instead it sought a balanced
(but bourgeois) viewpoint
on economics through the total sum of all the entries, not through any
one of them.

(26)Michael
Parkin, "Inflation", entry in Vol. 2 of The New Palgrave, "E
to J", p. 832.

(35)For
more on money illusion in establishment environmental economics and on
the type
calculations in Nordhaus' book A Question of Balance: Weighing the
Options on Global
Warming Policies, see "Market lunacy: the use of financial
calculation to answer material
questions" in "THE CARBON TAX: Another futile attempt at a free-market
solution to global
warming" in Communist Voice #42, August 2008
(www.communistvoice.org/42cCarbonTax.html).

(37)The
leftover or surplus product equals the entire production of means of
production minus the
amount needed to replace used up means of production in both
sectors. This is not an equivalent
for either the profits or surplus value obtained by this sphere of
production: this leftover product
is simply the surplus over the total use of the product in the economic
cycle. Similarly for the
leftover consumer goods.

(38)The C
row represents the production of means of production, which is also the
concrete form
of the constant capital of both sectors of production. The V row
represents the production of
consumer goods, which is also the concrete form of the variable capital
of both sectors of
production. The VAL column gives the total value of the production of
the various rows.